Preheat oven to 425°. Spray 13x9-inch glass or ceramic baking dish with nonstick cooking spray. In a large nonstick skillet, cook beef and garlic over medium-high heat 7 to 8 minutes or until beef is no longer pink, stirring frequently. Stir in 3 tablespoons flour, tomato paste, thyme, 1/ teaspoon salt and 3/4 teaspoon pepper. Reserve 2 tablespoons broth; stir remaining broth into skillet. Heat to simmering and cook 2 minutes. Spread beef mixture evenly in bottom of prepared dish.
In the same skillet, cook mushrooms, onion, and remaining 1/2 teaspoon salt and 3/4 teaspoon pepper over medium-high heat 5 to 6 minutes or until onion and mushroom are tender, stirring occasionally. Fold in peas and carrots and remaining 2 tablespoons broth. Spread vegetable mixture evenly over beef mixture.
In a medium microwave-safe bowl, heat potatoes in microwave on high 1 minute to soften. Stir potatoes; spread evenly over vegetable mixture.
Bake pie 20 to 25 minutes or until sides begin to bubble. Let stand 15 minutes before cutting.